Question

Paul has $70,000 to invest. His intent is to earn 15% interest on his investment. He can invest part of his money at 6% interest and part at 18% interest. How much does Paul need to invest in each option to make a total 15% return on his $70,000?6% interest $ 18% interest $

Answer 1

Given:

Paul has $70,000 to invest.

He invests a part of his money at 6% interest and part at 18% interest.

He needs to earn 15% interest on his investment.

To find:

The investment in each option.

Step-by-step explanation:

Let x be the amount invested in 18% interest.

Let (70000 - x) be the amount invested in 6% interest.

According to the problem,

Let us frame it as an equation as follows,

`6\%\text{ }of\text{ }(70000-x)+18\%\text{ }ofx=15\%\text{ }of\text{ }70000`

Solving for x, we get

`\begin{gathered} (6)/(100)(70000-x)+(18)/(100)x=(15)/(100)(70000) \\ (6(70000)-6x+18x)/(100)=(15(70000))/(100) \\ 420000+12x=1050000 \\ 12x=1050000-420000 \\ 12x=630000 \\ x=(630000)/(12) \\ x=52500 \end{gathered}`

So, the amount invested on 18% interest is $52500.

The amount invested on 6% interest is,

`70000-52500=\text{ \$}17500`

Final answer:

• The amount invested on 6% interest is $17500.

,

• The amount invested on 18% interest is $52500.